I was wondering, when do two ellipsoids colide? Ellipsoid ist acctualy just a sphere with 3 radi (radius), but just the radius can not be enough, because it is possible to place 2 ellipsoids in space so that the more than one raidus collide but the spheres are rotated so, that they do not colide. Imagine two eggs together, when you rotate one 30 degress up and the other 30 degrees down they do not collide but when you rotate them back to 0 they hit.

In my oppinion: the radius check is not enough. What to do?

And for a hybrid analytic/geometric perspective, have a look at David Eberly’s book, “3D Game Engine Design” (an excellent reference for all sorts of things in 3D).

Just a few things off the top of my head … I’m sure google has more to offer in the area of collision detection.